hours. He exercises by walking, jogging and running. His speeds while walking, jogging and running in
the ratio 1 : 2: 4. Which of the following statements
are true?
I. If he spends equal time on the three activities,
then he runs twice the distance that he jogs.
II. If he runs at 8 km per hour and distance
covered by running and jogging together is
12 km, then he walks a distance of 1 km in
1 hour.
III. If the time for which he walks, jogs and runs is
in the ratio 2 : 2 : 1 and he covers a total
distance of 10 km, then his speeds while
walking, jogging and running are 2 km/hr,
4 km/hr and 8 km/hr respectively.
I. Ratio of speed = 1 : 2 : 4
If equal time is spent on each of these, then
ratio of distance = 1 : 2 : 4
So, Sachin runs twice the distance that he jogs.
Thus, I is true.
II. He runs at 8 km/hr and therefore walks at
2 km/hr.
Hence II is not true.
III. Ratio of speed = 1 : 2 : 4
Ratio of time = 2: 2 : 1
Ratio of distance = 2 x l: 2 x 2 : 4 x 1
= 2: 4: 4
If Sachin covers a total distance of 10 km,
then he
Thus, III is true.
Thus, III is true.
36t + 48t - 16 = 68
t = 1 hr.
⇒ They meet at a distance of
⇒ 10 x 60 x 60 = 36000 m i.e., 36 km from A.
where T1 and T2 are time taken by trains A and B
to cover the whole distance
and 
Solving equations (i) and (ii), we get
T1 = 10 hrs. and T2 = 9 hrs.
Required distance
= A(ΔOAP) + A(ΔBXA) + A(▢APQX)
= 7.5 km.